Chip Somodevilla/Getty Images(WASHINGTON) -- Many colleges and universities are not properly reporting or investigating cases of sexual assaults on campuses.

That’s according to a new anonymous report on 350 institutions of higher education in the U.S.

At a news conference Wednesday, Senator Claire McCaskill said about a third of colleges aren't training campus police, students or faculty on how to deal with sexual assault cases, and admit they only investigate about half of all reports.

The Missouri Democrat said the survey found that 41 percent of the schools surveyed had not conducted a single investigation in the last five years.

“This survey shows that there are way too many schools that are failing and just about every institution in the country has room for improvement,” McCaskill said.

The report also found that 43 percent of the nation’s largest public schools allow students to help adjudicate sexual assault cases and 22 percent of the institutions permit athletic departments to have oversight of sexual assault cases involving athletes.

McCaskill said of that finding, "...I don't need to explain why that is a big problem."